The logarithmic integral function li(z) has a cut along the negative real axis which causes therein a discontinuity in the imaginary part of li(z). The real part of li(z), however, is well behaved for any real z, except the singularity at z=+1. At z=-1, real(li(z)) attains its absolute maximum, and also its only local maximum, on the real interval (-infinity,+1). The corresponding imaginary part is described in A257820.